Melt butter in a large pot over medium heat. Add shallots and 1 1/2 teaspoons salt, and saute, stirring occasionally, until tender and caramelized, 25 to 30 minutes. Add wine, and cook until it evaporates. Add bay leaf and broths, and bring to a boil. Reduce heat, and simmer until soup is reduced by one-third, 25 to 30 minutes. Season with salt and pepper.
Meanwhile, heat oil in a saute pan over medium heat. Add chestnuts, and saute until crisp, about 8 minutes. Transfer to a bowl; let cool. Add cheese and parsley, and toss with a fork.
Ladle soup into 6 bowls; top each with chestnut mixture.